Electronic antenna systems are utilized in systems that determine the attitude of an object or vehicle with respect to a fixed reference. In determining attitude, the difference in phase measurements between at least two antennas receiving an electromagnetic signal (such as from a satellite) is observed in order to calculate an attitude. The phase center of an antenna is a point on or near the surface of the antenna to which all of the phase measurements are referenced. For an ideal antenna, it is assumed that the antenna may be rotated about its phase center without affecting phase measurements. In practice, however, the position of the phase center varies with the angle of incidence of the incoming electromagnetic signal with respect to the antenna. If two antennas in an attitude determination system are precisely matched and mounted with the same orientation, then variations in the phase centers will cancel. However, this is often difficult to achieve in practice. As a result, phase measurements may be biased as much as ten millimeters. For an attitude system with limited baseline length and limited satellite visibility, phase measurement bias due to variations in antenna phase centers can produce significant errors in attitude calculations.
The differential phase map is the phase measurement error as a function of the angle of arrival of the incoming electromagnetic wave. The phase map is used for compensation that is necessary for accurate attitude determination. Variations in the phase center of an antenna can be compensated by assuming a fixed average phase center and then modeling a deterministic bias in the phase center where the bias is a function of the angle of incidence of the incoming electromagnetic signal. Typically, phase measurement errors (i.e. bias) in the antenna phase reception pattern may be determined by measuring the antenna phase reception pattern in an anechoic chamber. The phase measurement errors may then be subtracted from phase measurement data to compensate for the phase center bias. Since the bias is a function of the angle of incidence, at least an approximate attitude must be known before bias compensation may be utilized, which is not difficult to realize in practice. However, using an anechoic chamber to determine phase measurement errors is expensive, and it is often difficult to reproduce the antenna mounting arrangements of real systems in an anechoic chamber. Thus, there lies a need for an alternative, inexpensive method for determining phase measurement error in an antenna system that accurately models the antenna system configuration for which the phase measurement error is utilized.